The velocity of light in an electro-optic (EO) material, such as lithium niobate, depends upon the electric field in the material. This effect is utilized in the Mach-Zehnder integrated optic voltage-to-optical-amplitude modulator, one form of which is described in F. J. Leonberger, Optics Letters, 5, 312 (1980). The device described by Leonberger is fabricated on a substrate of X-cut lithium niobate with waveguide propagation in the Y direction. Electrodes are spaced across a branch of the waveguide in the Z direction, so as to impose an electric field in the Z direction on the waveguide material. The relationship between the crystal axes of the lithium niobate and the direction of the electric field is such that a significant EO effect is obtained on light traveling in the direction of waveguide propagation.
A somewhat more complex interferometer is shown in FIG. 1 of the accompanying drawings. The modulator shown in FIG. 1 comprises a substrate 2 of crystalline EO material on which is formed an optical waveguide 4. The waveguide extends between an input end 6 and an output end 8, and is divided into two parallel branches 10a and 10b. The waveguide is coupled at its input end by a single mode optical fiber 14 to a laser source 12, including a laser diode, and is coupled at its output end by a single mode fiber 18 to an optical detector 20, including a photodiode. The substrate 2 carries a bias electrode structure comprising electrodes 22a, 22b and 22c and an interferometer electrode structure comprising electrodes 24a, 24b and 24c. Each of the electrode structures forms two capacitors connected in parallel, with the two branches of the waveguide electrically stressed by the fields in the two capacitors respectively. The bias electrodes 22 are connected to a variable DC bias source, by way of terminals 26, whereas the interferometer electrodes 24 are connected to a source of a signal to be measured, such as a logic analyzer probe, by way of terminals 30. It can be seen that the two branches 10a and 10b are subjected to equal and opposite electric fields by each of the electrode structures. The orientation of the electric fields established by means of electrodes 22 and 24 relative to the crystal axes of the selected EO material is such that a significant EO effect is obtained on light traveling in the direction of waveguide propagation.
The phase of light leaving one of the branches 10a and 10b depends upon the integral with respect to distance of the electric field to which the branch is exposed. If the electric field is uniform over the length of each electrode structure, the portion of this integral that is attributable to each electrode structure is equal to the product of the length of the electrode structure times the electric field. Since the two waveguide branches are exposed to equal and opposite electric fields by each of the electrode structures, a differential phase shift .phi..sub.B occurs between the branches 10a and 10b due to the bias electrodes 22 and a differential phase shift .phi..sub.P occurs due to the interferometer electrodes 24. The phase shifts .phi..sub.i are related to the applied voltages V.sub.i by .phi..sub.i =K.sub.i L.sub.i V.sub.i, where K.sub.i is a constant that is dependent upon the electro-optic properties of the substrate and on the electrode structure and L.sub.i is the electrode length in the light propagation direction. It can be shown that the optical intensity I.sub.out at the output end 8 is related to the intensity I.sub.in at the input end 6 by: EQU I.sub.out =I.sub.in [1+cos (.phi..sub.B +.phi..sub.P)]/2 (1)
By appropriate selection of L.sub.B and adjustment of V.sub.B, .phi..sub.B can be made equal to 270.degree., so that EQU I.sub.out =I.sub.in (1+sin .phi..sub.P)/2 (2)
Therefore, the voltage output of the photodetector 20, which is a function of I.sub.out, is a measure of the probe voltage V.sub.P.
Since the phase shift .phi..sub.P is proportional to L.sub.P V.sub.P, it is possible to increase the voltage sensitivity .phi..sub.P V.sub.P by increasing the length L.sub.P of the interferometer electrode structure. However, the input capacitance C.sub.P of the interferometer electrode structure is proportional to L.sub.P. Therefore, if L.sub.p is increased the input capacitance C.sub.P also increases. Since the bandwidth of the signals that can be sensed is inversely proportional to the input capacitance C.sub.p, an increase in L.sub.P causes a reduction in bandwidth of the interferometer electrode structure.